A standard deck of 52 playing cards has 13 cards in each of four suits: Red Hearts, Red Diamonds, Black Spades and Black Clubs. In each suit there is an Ace, 2, 3, 4,
5, 6, 7, 8, 9, 10, Jack, Queen, King. The Jack, Queen and King are called Face Cards. Evan selects eight cards from the deck: two red queens, queen of clubs, both red aces, ace of spades and both black jacks. What is the probability that the ninth
randomly selected card will be a black king? Express your answer as a simplified
(common) fraction.